西部寒区岩体工程在冻融与循环荷载共同作用下易引发工程地质灾害，探明岩石在两者共同作用下的损伤机理和破坏前兆信息对灾害防治具有重要意义。本文以粗粒砂岩为研究对象，首先对其进行冻融循环试验，而后开展单轴压缩和循环加卸载试验，力学试验全过程采用声发射系统实时监测。分析冻融循环作用下岩石的力学特性；对冻融砂岩分级循环加载和卸载过程中的能量演化规律进行研究，并基于耗散能建立损伤模型；分析声发射b值演化规律，借助临界慢化理论探究声发射特征参数的临界慢化特征，得到冻融粗粒砂岩破坏前兆信息。主要研究结论如下：

（1）通过冻融循环、单轴压缩和分级循环加卸载试验，揭示冻融循环后粗粒砂岩的力学特性。随冻融次数的增加：纵波波速呈指数型函数降低，岩样初始冻融损伤加剧；单轴压缩抗压强度降低，承载力减弱，轴向变形增加，砂岩延性增强。在分级循环加卸载试验中：循环荷载使冻融次数较少的砂岩抗压强度较单轴压缩有所提高，冻融次数较多的砂岩有所减小；弹性模量整体呈增大趋势，残余应变在每个应力等级首次循环加卸载时显著增加，增幅随加载等级的增加逐渐减小，累积残余应变呈阶梯状增长；在相同循环加卸载次数下，冻融次数越多岩样弹性模量越小，累积残余变形越大。通过裂纹分类方法，统计两种加载方式下不同冻融次数岩样拉伸裂纹和剪切裂纹所占比例，拉伸裂纹占比远高于剪切裂纹，冻融循环和循环荷载未能改变拉伸裂纹的主导地位，所有岩样均为拉剪混合破坏模式。

（2）计算循环加卸载过程中砂岩的能量密度，分析能量演化特征。总能量密度和耗散能量密度随加卸载次数增加呈‘U’型递增，弹性能量密度呈台阶式增长，弹性能和耗散能在加载破坏阶段的差值随冻融次数增多逐渐减小。各累积能量密度随加载比呈指数型函数增长，弹性能、耗散能和总能量密度之间存在正线性相关关系。耗能系数随冻融次数增加而增大，储能系数呈相反变化趋势。基于耗散能建立损伤模型，表征损伤演化过程。该模型考虑了初始冻融损伤效应，冻融次数越多初始损伤值越大。损伤演化曲线呈非线性增长，破坏前损伤值增量最大；相同应力等级下，冻融次数越多曲线增加速率越慢，破坏越缓和，这与冻融循环增强砂岩的延性相关。

（3）声发射振铃计数能较好的反映砂岩内部损伤状态，振铃计数峰值与每个循环加卸载应力峰值相对应，卸载过程产生少量振铃计数。岩样破坏前振铃计数激增，累计振铃计数曲线随冻融次数增加在峰后阶段变缓。对声发射特征参数RA值和AF值分析，发现在单轴压缩和循环加卸载破坏前，RA值密集出现并突增，RA值在破坏前的显著增多表明剪切裂纹快速发展。

（4）基于声发射基本参数计算声发射b值，借助临界慢化理论探究失稳破坏前兆特征。首先分析了窗口长度和滞后步长对声发射b值、临界慢化特征参数方差和自相关系数计算结果的影响，表明各参数在不同窗口长度或滞后步长下得到的结果大小有所不同，但变化趋势基本保持一致，可忽略其对前兆特征的影响。在单轴压缩和加卸载破坏前，声发射b值突降，方差和自相关系数突增，通过前兆识别确定其突变点并作为破坏前兆点，前兆点均出现在峰值应力之前，可有效对粗粒砂岩破坏进行预警预报。

The rock mass engineering in the western cold region is easy to cause engineering geological disasters under the combined action of freeze-thaw and cyclic load. It is of great significance to explore the damage mechanism and failure precursor information of rock under the combined action of both for disaster prevention and control. In this paper, coarse-grained sandstone is taken as the research object. Firstly, the freeze-thaw cycle test is carried out, and then the uniaxial compression and cyclic loading and unloading test are carried out. The whole process of mechanical test is monitored in real time by acoustic emission system. The mechanical properties of rock under freeze-thaw cycles are analyzed. The energy evolution law of freeze-thaw sandstone during graded cyclic loading and unloading was studied, and the damage model was established based on dissipated energy. The evolution law of b value of acoustic emission is analyzed, and the critical slowing down characteristics of acoustic emission characteristic parameters are explored by means of critical slowing down theory, and the precursor information of freeze-thaw coarse-grained sandstone failure is obtained. The main conclusions are as follows :

(1) Through freeze-thaw cycles, uniaxial compression and graded cyclic loading and unloading tests, the mechanical properties of coarse-grained sandstone after freeze-thaw cycles are revealed. With the increase of freeze-thaw times, the longitudinal wave velocity decreases exponentially, and the initial freeze-thaw damage of rock samples increases. The uniaxial compressive strength is reduced, the bearing capacity is weakened, the axial deformation is increased, and the ductility of sandstone is enhanced. In the graded cyclic loading and unloading test, the compressive strength of sandstone with fewer freeze-thaw cycles is higher than that of uniaxial compression, and the sandstone with more freeze-thaw cycles is reduced. The elastic modulus increases as a whole, and the residual strain increases significantly at the first cyclic loading and unloading of each stress level. The increase gradually decreases with the increase of the loading level, and the cumulative residual strain increases in a stepwise manner. Under the same number of cyclic loading and unloading times, the more the number of freeze-thaw cycles, the smaller the elastic modulus of the rock sample, and the greater the cumulative residual deformation. Through the crack classification method, the proportion of tensile cracks and shear cracks of rock samples with different freeze-thaw times under two loading methods is counted. The proportion of tensile cracks is much higher than that of shear cracks. Freeze-thaw cycles and cyclic loads do not change the dominant position of tensile cracks. All rock samples are tensile-shear mixed failure modes.

(2) The energy density of sandstone during cyclic loading and unloading is calculated, and the energy evolution characteristics are analyzed. The total energy density and dissipated energy density increase in a ' U ' shape with the increase of loading and unloading times, and the elastic energy density increases step by step. The difference between elastic energy and dissipated energy in the loading failure stage gradually decreases with the increase of freezing and thawing times. The cumulative energy density increases exponentially with the loading ratio, and there is a positive linear correlation between elastic energy, dissipated energy and total energy density. The energy dissipation coefficient increases with the increase of the number of freeze-thaw cycles, and the energy storage coefficient shows the opposite trend. Based on the dissipated energy, the damage model is established to characterize the damage evolution process. The model considers the initial freeze-thaw damage effect, and the more the number of freeze-thaw cycles, the greater the initial damage value. The damage evolution curve increases nonlinearly, and the increment of damage value before failure is the largest. Under the same stress level, the more the number of freeze-thaw cycles, the slower the increase rate of the curve and the more moderate the damage, which is related to the ductility of sandstone enhanced by freeze-thaw cycles.

(3) Acoustic emission ringing count can better reflect the internal damage state of sandstone. The peak value of ringing count corresponds to the peak value of each cyclic loading and unloading stress, and a small amount of ringing count is generated during the unloading process. Before the rock sample was destroyed, the ringing count increased sharply, and the cumulative ringing count curve slowed down in the post-peak stage with the increase of freeze-thaw times. The analysis of acoustic emission characteristic parameters RA value and AF value shows that RA value appears intensively and increases sharply before uniaxial compression and cyclic loading and unloading failure. The significant increase of RA value before failure indicates the rapid development of shear cracks.

(4) Based on the basic parameters of acoustic emission, the b value of acoustic emission is calculated, and the precursor characteristics of instability failure are explored by means of critical slowing down theory. Firstly, the influence of window length and lag step size on the calculation results of acoustic emission b value, variance of critical slowing down characteristic parameters and autocorrelation coefficient is analyzed. It shows that the results of each parameter under different window length or lag step size are different, but the change trend is basically the same, and its influence on precursor characteristics can be ignored. Before uniaxial compression and loading and unloading failure, the b value of acoustic emission decreases suddenly, and the variance and autocorrelation coefficient increase suddenly. The mutation point is determined by precursor identification and used as the precursor point of failure. The precursor points all appear before the peak stress, which can effectively warn and predict the failure of coarse-grained sandstone.

[1] 陈卫忠, 谭贤君, 于洪丹, 等. 低温及冻融环境下岩体热、水、力特性研究进展与思考[J]. 岩石力学与工程学报, 2011, 30(07): 1318-1336.

[2] 高峰, 周科平, 熊信. 我国高海拔寒区金属矿产资源开采现状及关键问题[J]. 矿业研究与开发, 2022, 42(10): 1-5.

[3] Xie L L, Qu Z. On civil engineering disasters and their mitigation[J]. Earthquake Engineering and Engineering Vibration, 2018, 17: 1-10.

[4] Xiao P, Liu H X, Zhao G Y. Characteristics of ground pressure disaster and rockburst proneness in deep gold mine[J]. Lithosphere, 2023, 2022(Special 11): 9329667.

[5] 杨志全, 甘进, 樊详珑, 等. 岩石冻融损伤机理研究进展及展望[J]. 防灾减灾工程学报, 2023, 43(01): 176-188.

[6] 黄锋, 周洋, 彭焱森, 等. 循环荷载下花岗岩强度及变形特征试验研究[J]. 地下空间与工程学报, 2021, 17(02): 356-364.

[7] Shen Y J, Yang H W, Jin L, et al. Fatigue deformation and energy change of single-joint sandstone after freeze-thaw cycles and cyclic loadings[J]. Frontiers in Earth Science, 2019, 7: 333.

[8] 冯增朝, 吕兆兴, 赵阳升. 岩石破坏短临预报研究进展——岩石破坏短临预报竞赛评述[J]. 岩石力学与工程学报, 2022, 41(12): 2522-2529.

[9] Kandula N, Cordonnier B, Boller E, et al. Dynamics of microscale precursors during brittle compressive failure in carrara marble[J]. Journal of Geophysical Research: Solid Earth, 2019, 124(6): 6121-6139.

[10] Wang C L, Lu Z J, Liu L, et al. Predicting points of the infrared precursor for limestone failure under uniaxial compression[J]. International Journal of Rock Mechanics and Mining Sciences, 2016, 88: 34-43.

[11] Qiu L M, Liu Z T, Wang E Y, et al. Early-warning of rock burst in coal mine by low-frequency electromagnetic radiation[J]. Engineering Geology, 2020, 279: 105755.

[12] 唐巨鹏, 任凌冉, 潘一山, 等. 深部煤与瓦斯突出孕育全过程声发射前兆信号变化规律研究[J]. 实验力学, 2021, 36(06): 827-837.

[13] 王腾飞, 李远耀, 徐勇, 等. 基于声发射试验的红层砂岩损伤演化特性分析[J]. 地质科技情报, 2019, 38(04): 247-254.

[14] Wei Y, Li Z H, Kong X G, et al. The precursory information of acoustic emission during sandstone loading based on critical slowing down theory[J]. Journal of Geophysics and Engineering, 2018, 15(5): 2150-2158.

[15] Scheffer M, Bascompte J, Brock W A, et al. Early-warning signals for critical transitions[J]. Nature, 2009, 461(7260): 53-59.

[16] 魏洋, 李忠辉, 孔祥国, 等. 砂岩单轴压缩破坏的临界慢化特征[J]. 煤炭学报, 2018, 43(02): 427-432.

[17] Li H R, Shen R X, Qiao Y F, et al. Acoustic emission signal characteristics and its critical slowing down phenomenon during the loading process of water-bearing sandstone[J]. Journal of Applied Geophysics, 2021, 194: 104458.

[18] Guo H, Ji M, Zhang Y, et al. Study of mechanical property of rock under uniaxial cyclic loading and unloading[J]. Advances in Civil Engineering, 2018, 2018.

[19] Zhao B, Liu D, Li Z, et al. Mechanical behavior of shale rock under uniaxial cyclic loading and unloading condition[J]. Advances in Civil Engineering, 2018, 2018.

[20] Yang D, Zhang D, Niu S, et al. Experiment and study on mechanical property of sandstone post-peak under the cyclic loading and unloading[J]. Geotechnical and Geological Engineering, 2018, 36: 1609-1620.

[21] Song Z, Konietzky H, Wu Y, et al. Mechanical behaviour of medium-grained sandstones exposed to differential cyclic loading with distinct loading and unloading rates[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2022, 14(6): 1849-1871.

[22] 李旭, 张鹏超. 循环加卸载下黄砂岩力学特性和能量演化规律[J]. 长江科学院院报, 2021, 38(04): 124-131.

[23] 贾蓬, 王茵, 李博, 等. 高温遇水冷却岩石循环加卸载力学性能试验研究[J]. 北京理工大学学报, 2023, 43(02): 126-134.

[24] 刘忠玉, 董旭 张旭阳. 分级循环荷载下层理煤岩力学特性试验研究[J]. 岩石力学与工程学报, 2021, 40(S1): 2593-2602.

[25] 苗胜军, 王辉, 黄正均, 等. 不同循环上限荷载下泥质石英粉砂岩力学特性试验研究[J]. 工程力学, 2021, 38(07): 75-85.

[26] Li T, Pei X, Wang D, et al. Nonlinear behavior and damage model for fractured rock under cyclic loading based on energy dissipation principle[J]. Engineering Fracture Mechanics, 2019, 206: 330-341.

[27] Liu X S, Ning J G, Tan Y L, et al. Damage constitutive model based on energy dissipation for intact rock subjected to cyclic loading[J]. International journal of rock mechanics and mining sciences, 2016, 85: 27-32.

[28] Wang H, Li J. Mechanical behavior evolution and damage characterization of coal under different cyclic engineering loading[J]. Geofluids, 2020, 2020: 1-19.

[29] 杨科, 张寨男, 池小楼, 等. 循环载荷下含水砂岩裂纹演化与损伤特征试验研究[J]. 岩土力学, 2022, 43(07): 1791-1802.

[30] 徐颖, 李成杰, 郑强强, 等. 循环加卸载下泥岩能量演化与损伤特性分析[J]. 岩石力学与工程学报, 2019, 38(10): 2084-2091.

[31] Liang D, Zhang N, Xie L, et al. Damage and fractal evolution trends of sandstones under constant-amplitude and tiered cyclic loading and unloading based on acoustic emission[J]. International Journal of Distributed Sensor Networks, 2019, 15(7): 1550147719861020.

[32] Liu X, Zhang H, Wang X, et al. Acoustic emission characteristics of graded loading intact and holey rock samples during the damage and failure process[J]. Applied Sciences, 2019, 9(8): 1595.

[33] 吴成龙, 苏占东, 夏京, 等. 基于Felicity效应的砂岩损伤特性的试验研究[J]. 实验力学, 2019, 34(04): 721-728.

[34] 裴向军, 朱凌, 崔圣华, 等. 加卸载条件下含缺陷岩石声发射响应特征研究[J]. 岩石力学与工程学报, 2020, 39(S1): 2602-2611.

[35] 谢和平, 彭瑞东, 鞠杨, 等. 岩石破坏的能量分析初探[J]. 岩石力学与工程学报, 2005(15): 2603-2608.

[36] 赵忠虎, 鲁睿, 张国庆. 岩石破坏全过程中的能量变化分析[J]. 矿业研究与开发, 2006(05): 8-11.

[37] He Z, Gong F, Wu W, et al. Experimental investigation of the mechanical behaviors and energy evolution characteristics of red sandstone specimens with holes under uniaxial compression[J]. Bulletin of Engineering Geology and the Environment, 2021, 80: 5845-5865.

[38] Gong F, Zhang P, Xu L. Damage constitutive model of brittle rock under uniaxial compression based on linear energy dissipation law[J]. International Journal of Rock Mechanics and Mining Sciences, 2022, 160: 105273.

[39] 张亮, 王桂林, 雷瑞德, 等. 单轴压缩下不同长度单裂隙岩体能量损伤演化机制[J]. 中国公路学报, 2021, 34(01): 24-34.

[40] 王桂林, 张亮, 许明, 等. 单轴压缩下非贯通节理岩体损伤破坏能量演化机制研究[J]. 岩土工程学报, 2019, 41(04): 639-647.

[41] 耿凯强, 李晓丽. 单轴压缩下红色砒砂岩水泥土的能量演化机制研究[J]. 水文地质工程地质, 2020, 47(05): 134-141.

[42] 武旭, 张丽媛, 孙景来, 等. 单轴压缩下交叉裂隙花岗岩变形与能量演化分析[J]. 北京交通大学学报, 2021, 45(03): 77-83.

[43] Sun B, Yang H, Fan J, et al. Energy Evolution and Damage Characteristics of Rock Materials under Different Cyclic Loading and Unloading Paths[J]. Buildings, 2023, 13(1): 238.

[44] Kong L, Xie H, Gao C, et al. Experimental and theoretical research on the anisotropic deformation and energy evolution characteristics of shale under uniaxial cyclic loading and unloading[J]. International Journal of Geomechanics, 2022, 22(11): 04022208.

[45] Liu X S, Ning J G, Tan Y L, et al. Damage constitutive model based on energy dissipation for intact rock subjected to cyclic loading[J]. International journal of rock mechanics and mining sciences, 2016, 85: 27-32.

[46] Meng Q, Liu J, Pu H, et al. Effects of cyclic loading and unloading rates on the energy evolution of rocks with different lithology[J]. Geomechanics for Energy and the Environment, 2023, 34: 100455.

[47] 郭红军, 季明, 孙中光, 等. 循环荷载作用下红砂岩能量演化特征研究[J]. 采矿与岩层控制工程学报, 2021, 3(04): 15-23.

[48] 李杨杨, 张士川, 文志杰, 等. 循环载荷下煤样能量转化与碎块分布特征[J]. 煤炭学报, 2019, 44(05): 1411-1420.

[49] 李利峰, 张晓虎, 邓慧琳, 等. 不同加载速率下砂岩的单轴压缩试验力学特性及能量演化规律[J]. 采矿与岩层控制工程学报, 2020, 2(04): 83-89.

[50] 吴再海, 宋朝阳, 谭杰, 等. 不同分级循环加卸载模式下岩石能量演化规律研究[J]. 采矿与安全工程学报, 2020, 37(04): 836-844+851.

[51] 汪泓, 杨天鸿, 刘洪磊, 等. 循环荷载下干燥与饱和砂岩力学特性及能量演化[J]. 岩土力学, 2017, 38(06): 1600-1608.

[52] 赵光明, 刘之喜, 孟祥瑞, 等. 高径比对砂岩能量积聚与耗散试验及分析方法[J]. 煤炭学报, 2022, 47(03): 1110-1121.

[53] 张磊, 李兵, 朱宝龙, 等. 红层泥岩加卸载力学特性与能量演化机制[J]. 西南交通大学学报, 2023, 58(03): 592-602+612.

[54] 徐金海, 张晓悟, 刘智兵, 等. 循环加卸载条件下煤岩组合体力学响应及能量演化规律[J]. 长江科学院院报, 2022, 39(05): 89-94.

[55] 孟庆彬, 王从凯, 黄炳香, 等. 三轴循环加卸载条件下岩石能量演化及分配规律[J]. 岩石力学与工程学报, 2020, 39(10): 2047-2059.

[56] Hardy H R. Applications of acoustic emission techniques to rock and rock structures: a state-of-the-art review[J]. Acoustic emissions in geotechnical engineering practice, STP, 1981, 750: 4-92.

[57] 张大伦. 声发射技术在国外岩石工程中的应用[J]. 岩石力学与工程学报, 1985(01): 77-83.

[58] Triantis D. Acoustic emission monitoring of marble specimens under uniaxial compression. Precursor phenomena in the near-failure phase[J]. Procedia Structural Integrity, 2018, 10: 11-17.

[59] Hou Z, Xiao F, Liu G, et al. Mechanical Properties and Acoustic Emission Characteristics of Unloading Instability of Sandstone under High Stress[J]. Minerals, 2022, 12(6): 722.

[60] Yang J, Mu Z L, Yang S Q. Experimental study of acoustic emission multi-parameter information characterizing rock crack development[J]. Engineering Fracture Mechanics, 2020, 232: 107045.

[61] Xu J, Jiang J, Zuo L, et al. Acoustic emission monitoring and failure precursors of sandstone samples under various loading and unloading paths[J]. Shock and Vibration, 2017, 2017.

[62] Li P, Cai M, Guo Q, et al. Investigation on acoustic emission characteristics of hole-joint contained granite under a compressive disturbance: experimental insights[J]. Lithosphere, 2022, 2022(Special 11): 3594940.

[63] 宋朝阳, 纪洪广, 张月征, 等. 不同粒度弱胶结砂岩声发射信号源与其临界破坏前兆信息判识[J]. 煤炭学报, 2020, 45(12): 4028-4036.

[64] 王小林, 温仕轩, 王煜东, 等. 高温作用下砂岩声发射特征及破坏前兆[J]. 长江科学院院报, 2023, 40(11): 118-124.

[65] 高保彬, 李回贵, 李化敏, 等. 含水煤样破裂过程中的声发射及分形特性研究[J]. 采矿与安全工程学报, 2015, 32(04): 665-670+676.

[66] 李庶林, 周梦婧, 高真平, 等. 增量循环加卸载下岩石峰值强度前声发射特性试验研究[J]. 岩石力学与工程学报, 2019, 38(04): 724-735.

[67] Li D X, Wang E Y, Kong X G, et al. Damage precursor of construction rocks under uniaxial cyclic loading tests analyzed by acoustic emission[J]. Construction and Building Materials, 2019, 206: 169-178.

[68] 付斌, 周宗红, 王海泉, 等. 大理岩单轴循环加卸载破坏声发射先兆信息研究[J]. 煤炭学报, 2016, 41(08): 1946-1953.

[69] Dakos V, Bascompte J. Critical slowing down as early warning for the onset of collapse in mutualistic communities[J]. Proceedings of the National Academy of Sciences, 2014, 111(49): 17546-17551.

[70] 晏锐, 蒋长胜, 张浪平. 汶川8.0级地震前水氡浓度的临界慢化现象研究[J]. 地球物理学报, 2011, 54(07): 1817-1826.

[71] Zhang Z, Li Y, Hu L, et al. Predicting rock failure with the critical slowing down theory[J]. Engineering Geology, 2021, 280: 105960.

[72] Zhang Z, Chen T, Ma K, et al. Precursory indicator for mode I fracture in brittle rock through critical slowing down analysis[J]. Shock and Vibration, 2020, 2020: 1-9.

[73] Li H, Shen R, Qiao Y, et al. Acoustic emission signal characteristics and its critical slowing down phenomenon during the loading process of water-bearing sandstone[J]. Journal of Applied Geophysics, 2021, 194: 104458.

[74] 魏洋, 李忠辉, 孔祥国, 等. 砂岩单轴压缩破坏的临界慢化特征[J]. 煤炭学报, 2018, 43(02): 427-432.

[75] 朱星, 刘汉香, 胡桔维, 等. 砂岩破坏声发射临界慢化前兆特征试验研究[J]. 岩土力学, 2022, 43(S1): 164-172.

[76] 朱星, 唐垚, 范杰, 等. 基于临界慢化理论的细砂岩破坏前兆试验研究[J]. 岩石力学与工程学报, 2022, 41(01): 53-61.

[77] 王桂林, 王润秋, 孙帆, 等. 单轴压缩下溶隙灰岩声发射RA-AF特征及破裂模式研究[J]. 中国公路学报, 2022, 35(08): 118-128.

[78] 葛振龙, 孙强, 王苗苗, 等. 基于RA/AF的高温后砂岩破裂特征识别研究[J]. 煤田地质与勘探, 2021, 49(02): 176-183.

[79] Gutenberg B, Richter C F. Frequency of earthquakes in California[J]. Bulletin of the Seismological society of America, 1944, 34(4): 185-188.

[80] Clauset A, Shalizi C R, Newman M E J. Power-law distributions in empirical data[J]. SIAM review, 2009, 51(4): 661-703.

[81] 李亚昊. 不同饱和度砂岩冻融损伤规律及预警模型研究[D]. 辽宁工程技术大学, 2021.